|
%I #7 Jan 11 2017 09:51:55
%S 7,119,4564,32900,1161895,8359127,295119412,2123188004,74959171399,
%T 539281396535,19039334418580,136975351534532,4835915983150567,
%U 34791200008377239,1228303620385828084,8836827826776286820,311984283662017185415,2244519476801168477687
%N Positive integers n such that (n+21)^3 - n^3 is a square.
%H Colin Barker, <a href="/A263943/b263943.txt">Table of n, a(n) for n = 1..831</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,254,-254,-1,1).
%F a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5) for n>5.
%F G.f.: 7*x*(4*x^4+16*x^3-381*x^2-16*x-1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).
%e 7 is in the sequence because (7+21)^3 - 7^3 = 147^2.
%t LinearRecurrence[{1,254,-254,-1,1},{7,119,4564,32900,1161895},20] (* _Harvey P. Dale_, Jan 11 2017 *)
%o (PARI) Vec(7*x*(4*x^4+16*x^3-381*x^2-16*x-1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^30))
%Y Cf. A263942 (4), A263944 (28), A263945 (39), A263946 (52), A263947 (57), A263948 (61), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Oct 30 2015
|
